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Business Stats

(See attached file for full problem description)

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15 pts. 4. We want to develop a model to predict the selling price of a home based upon the assessed value. A sample of 30 recently sold single-family houses is selected. The results are as follows:
Observation Assessed Value (000) Selling Price(000)
1 78.17 94.10
2 80.24 101.90
3 74.03 88.65
4 86.31 115.50
5 75.22 87.50
6 65.54 72.00
7 72.43 91.50
8 85.61 113.90
9 60.80 69.34
10 81.88 96.90
11 79.11 96.00
12 59.93 61.90
13 75.27 93.00
14 85.88 109.50
15 76.64 93.75
16 84.36 106.70
17 72.94 81.50
18 76.50 94.50
19 66.28 69.00
20 79.74 96.90
21 72.78 86.50
22 77.90 97.90
23 74.31 83.00
24 79.85 97.30
25 84.78 100.80
26 81.61 97.90
27 74.92 90.50
28 79.98 97.00
29 77.96 92.00
30 79.07 95.90
Develop a regression equation to forecast the demand for paper given a level of sales.
a. How good is the model? Explain.
b. What does the y-intercept mean? Is that reasonable?
c. Interpret the meaning of the slope.
d. Forecast the selling price of a house with an assessed value of $65,000 and a house with an assessed value of $103,000. What concerns with accuracy do you have over these predictions
10 pts. 5. The manufacturer of soap is in the process of producing 48-ounce boxes of detergent. The automated filling device needs frequent checking to verify that it's actually putting 48 ounces in each box. Box weights are known to be normally distributed with a standard deviation of 0.2 ounces. A sample of 50 boxes is taken and found to have a mean of 47.6 ounces. If you use a .05 significance level, is the machine filling the boxes properly?
10 pts. 6. A gift shop is interested in charges made by credit card customers. The owner wants an estimate of the mean purchase amount for credit card customers that are within $1.00 of the actual population mean. The standard deviation is estimated at $4.75.
a. How large a sample is necessary for a 98% confidence level?
b. If the gift shop owner used a sample of 100 credit card customers what is the maximum tolerable error?
5 pts. 7. You are going to meet with a potential new client and help them set up a test to detect when a process goes out of control. Discuss the issues that need to be considered in determining an appropriate significance level.
10 pts. 8. You are considering a new delivery system and wish to test whether delivery times are significantly different, on average, than your current system. It is well established that the mean delivery time of the current system is 2.38 days. A test of the new system shows that, with 48 observations, the average delivery time is 2.23 days with a standard deviation of 0.43 day. Test at the .05 significance level. Summarize your results in a brief memo to management.
10 pts. 9. Your bakery produces loaves of bread with "1 pound" written on the label. Here are the weights of randomly sampled loaves from today's production:
1.02, .97, .98, 1.1, 1.0, 1.02, .98, 1.03, 1.03, 1.0, 1.02, 1.06
Test the claim on the package at the .02 significance level.
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(See attached file for full problem description)

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Solution Summary

5 pts. 4. We want to develop a model to predict the selling price of a home based upon the assessed value. A sample of 30 recently sold single-family houses is selected. The results are as follows:
Observation Assessed Value (000) Selling Price(000)
1 78.17 94.10
2 80.24 101.90
3 74.03 88.65
4 86.31 115.50
5 75.22 87.50
6 65.54 72.00
7 72.43 91.50
8 85.61 113.90
9 60.80 69.34
10 81.88 96.90
11 79.11 96.00
12 59.93 61.90
13 75.27 93.00
14 85.88 109.50
15 76.64 93.75
16 84.36 106.70
17 72.94 81.50
18 76.50 94.50
19 66.28 69.00
20 79.74 96.90
21 72.78 86.50
22 77.90 97.90
23 74.31 83.00
24 79.85 97.30
25 84.78 100.80
26 81.61 97.90
27 74.92 90.50
28 79.98 97.00
29 77.96 92.00
30 79.07 95.90
Develop a regression equation to forecast the demand for paper given a level of sales.
a. How good is the model? Explain.
b. What does the y-intercept mean? Is that reasonable?
c. Interpret the meaning of the slope.
d. Forecast the selling price of a house with an assessed value of $65,000 and a house with an assessed value of $103,000. What concerns with accuracy do you have over these predictions
10 pts. 5. The manufacturer of soap is in the process of producing 48-ounce boxes of detergent. The automated filling device needs frequent checking to verify that it's actually putting 48 ounces in each box. Box weights are known to be normally distributed with a standard deviation of 0.2 ounces. A sample of 50 boxes is taken and found to have a mean of 47.6 ounces. If you use a .05 significance level, is the machine filling the boxes properly?
10 pts. 6. A gift shop is interested in charges made by credit card customers. The owner wants an estimate of the mean purchase amount for credit card customers that are within $1.00 of the actual population mean. The standard deviation is estimated at $4.75.
a. How large a sample is necessary for a 98% confidence level?
b. If the gift shop owner used a sample of 100 credit card customers what is the maximum tolerable error?
5 pts. 7. You are going to meet with a potential new client and help them set up a test to detect when a process goes out of control. Discuss the issues that need to be considered in determining an appropriate significance level.
10 pts. 8. You are considering a new delivery system and wish to test whether delivery times are significantly different, on average, than your current system. It is well established that the mean delivery time of the current system is 2.38 days. A test of the new system shows that, with 48 observations, the average delivery time is 2.23 days with a standard deviation of 0.43 day. Test at the .05 significance level. Summarize your results in a brief memo to management.
10 pts. 9. Your bakery produces loaves of bread with "1 pound" written on the label. Here are the weights of randomly sampled loaves from today's production:
1.02, .97, .98, 1.1, 1.0, 1.02, .98, 1.03, 1.03, 1.0, 1.02, 1.06
Test the claim on the package at the .02 significance level.
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